Peter Bodo has been covering tennis for over 35 years, mostly recently for ESPN. He is a former WTA Writer of the Year and the author of numerous books, including the classic "The Courts of Babylon" and the New York Times bestseller (with Pete Sampras), "A Champion's Mind."

NEW YORK -- Rafael Nadal has spent a lot of time on the run. He has won, and won a lot, just as he did Sunday afternoon, but he has never caught his longtime nemesis -- no matter how close he has come.

Nadal took another step in catching Roger Federer on the all-time Grand Slam list by clinically dissecting the game of 6-foot-8 South African Kevin Anderson 6-3, 6-3, 6-4 to win his third US Open title. It was Nadal's 16th Grand Slam championship and second this year.

As impressive as that is, it still leaves Nadal three major titles behind Federer in the chase. In other words, Nadal failed to pick up any ground from the end of last season, as both men left the 2017 season with two Grand Slam titles in hand.

This was the first time in their careers that Rafael Nadal and Roger Federer both won two majors in the same season. Matthew Stockman/Getty Images

Like Nadal, the Swiss icon -- a quarterfinal loser here -- was in the same disheartening situation as Nadal during the second half of 2016. Both men were injured and thought by some to be in an irreversible eclipse. But they rose from the ashes like a pair of squawking, pecking phoenixes to remind us that their rivalry might be the greatest story ever told in men's tennis.

Nadal appreciates his careerlong tug-of-war for superiority with Federer.

"I feel lucky to be part of it [the rivalry]," Nadal said afterward. "We competed for such a long time for first and second in the sport, and competed for the most important events."

Nadal said he doesn't think much of the race for the Slam King crown, adding, "I do my way, he does it his way. I'm very happy with all the things that are happening to me. I won this [US Open] title again. I have this trophy with me."

Nadal, 31, is younger than Federer by almost five years. Nadal always has been the hunter, but he has been resolute throughout the chase -- unwilling to give up, no matter how hopeless it sometimes appeared or how elusive his quarry. The hunt has lit up tennis since the men first met more than 13 years and 37 matches ago, when an 18-year-old Spanish upstart beat Federer at the 2004 Miami Masters.

Over the years, the rivalry has painted legions of faces with broad smiles of appreciation and expressions of sheer amazement -- and a sea's worth of tears. It also has weathered the interruption created by Novak Djokovic, a slump by Nadal and other missed opportunities, both large and small.

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Rafael Nadal made it three titles at Flushing Meadows by sweeping Kevin Anderson in the US Open final. The top-seeded Spaniard now has 16 career Grand Slam titles, trailing only Roger Federer's 19 for most all time.

Let's get this straight: Rafael Nadal, the oft-injured, shaken superstar from the past couple of years, won two majors and is the No. 1 player in the world in 2017? This season couldn't be any sweeter.

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Nadal denies actively thinking about chasing Federer in the Slam count, but he knows his numbers.

"I really never thought much about it," he said. "He has 19; I have 16. So, three is big difference. Let's see when we finish. Of course, if I had won two Grand Slams this year and he didn't win, we would be closer."

Except Federer did win, twice.

Fed's stunning win in Melbourne this year takes on special resonance. Nadal was beautifully positioned to claim the title, as he led Federer 3-1 in the fifth set. Had Nadal managed to hold the lead, the disparity in Grand Slam titles right now would be a razor-thin margin of 18-17.

Nadal's late-career resurgence includes a greater appreciation for good health and resolution -- and to never lose sight of the fact that playing tennis is supposed to be fun. It certainly would put a damper on his spirits if he stopped to stew over the fact that Federer checkmated him by engineering his own renaissance at exactly the same time.

"It's very close right now," Anderson said of the rivalry, after his loss to Nadal. "I mean, obviously, staying healthy would be the biggest obstacle [to Nadal getting closer]. Roger is obviously a few years older than him, but then he's had an amazing year."

The age factor might become critically important in the near future. The gap of almost five full years will favor Nadal in the twilight of their careers, the same way it once provided Federer with the advantage of greater experience and maturity.

As well, Nadal's superiority on clay is such that he seems almost a sure bet to add to his title count of 10 French Opens. Federer doesn't enjoy a comparable advantage anywhere.

There are other factors that could prevent Rafa from catching Roger. The chief among them will be the return of Djokovic and Andy Murray in 2018. But one of the great lessons we learned in this season is that nobody really knows what the future, even the very near future, will bring.

But if the past is any indication, it will deliver more of the rivalry that stands as the best symbol of the Big Four era. The hunt surely will go on. It always does.